A parallel beam of monochromatic light is used in a Young’s double slit experiment. The slits are separated by a distance d and the screen is placed parallel to the plane of the slits. Slow that if the incident beam makes an angle
θ=sin-1 λ2dwith the normal to the plane of the slits, there will be a dark fringe at the centre P0 of the pattern.
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It can be seen from the figure that the wavefronts reaching O from S1 and S2 will have a path difference of S2X. As the path difference is an odd multiple of λ/2, there will be a dark fringe at point P0.
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Explanation:
Let the two slits are S1 and S2 with separation d as shown in the attached figure.
It can be seen from the figure that the wavefronts reaching O from S1 and S2 will have a path difference of S2X
In ΔS1S2X
sinθ= S2X/S1S2
So path difference =S2X=S1S2 sinθ= d sinθ
=d x λ/2d =λ/2
As the path difference is an odd multiple of λ/2 there will be dark fringe at a point p.
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